String Theory and Vibrations

[Guest]

Dear all,

I attended a presentation on String Theory the other week. This was held by the physics department of a university near-by.

The role of vibrations sure was interesting, as were the many mathematical tricks used to make the theory work.

Sincerely,

S. Holmes

 

[DanishDynamite]

Uh....Ok. Thanks for sharing.

 

[Guest]

Uh....Ok. Thanks for sharing.

Dear DanishDynamite,

Don't give me any of your negative vibrations.

Sincerely,

S. Holmes

 

[LeFevre]

Dear all,

I attended a presentation on String Theory the other week. This was held by the physics department of a university near-by.

The role of vibrations sure was interesting, as were the many mathematical tricks used to make the theory work.

Sincerely,

S. Holmes

What university? Did you understand why many mathematical tricks were used to make the theory work? Did you follow the reasoning? It would probably go way over me, but it would've been fun to go.

 

[Denise]

So did you learn how the vibrations of the strings make certain sounds? Did you find out how the width of the strings make different notes? Plucking vs stroking with a bow, which was better?

 

[Guest]

Dear all,

The entire time I was thinking about "bad vibrations" often said by proponents of parasciences.

Here are some things I learned from the presentation. I don't claim to know what any of it means in any detail.

As a string moves through space, it sweeps out a cylinder

Position of string over time = center of mass + momentum + vibrations

Advantage: you just have one kind of particle

Uses complex geometry (ie. complex numbers)

In string theory, we can patch together complex cylinders to get a "thickening" of a Fenyman diagram, called a "worldsheet"

The interactions are built in

We can make sense of it in 26 dimensions

26 = 2 - (2/zeta(-1)), where zeta(-1) is the Riemann-Zeta function and = -1/12

24 of these 26 dimensions are to "wiggle" in

There is a mathematical trick to get rid of the infinite sums, but this introduces negative energy, which is the same thing as saying (by E = mc^2) imaginary mass, which are called "tachyons"

Strings are curved, so we get gravity for free

By supersymmetry, we can reduce n to 10 (from 26). This is closer to 4.

we can also eliminate tachyons

5 types of superstrings
1 open type
2 types of closed
2 types of heterotic (nicest ones)

These are all under "M-theory"

Quote: "Spacetime is a figment of a string's imagination"

Is there a theory bigger than these where these are special cases of it?

Sincerely,

S. Holmes

 

[Denise]

Dang it! I thought we were talking about string instruments. Having no formal or even good education on the string theory, I think I'll just watch.

 

[Dancing David]

String theory is way cool, it is still sorting itself out, the main problem is that the mathematical ramifications are so complex. There are like a huge number of ways strings can manifest, and the math is so complex that it is hard to tell the good candidates from the chaff. In the end it will sort into something that supports QM, I hope.

Peace
dancing David

 

[garys_2k]

2 types of heterotic (nicest ones)

Hetero-erotic strings? Those are used for certain swimsuits, right? And yes, those would be the nicest ones in my book, too.

 

[Vorticity]

...
where zeta(-1) is the Riemann-Zeta function and = -1/12
...

This part jumped out at me.
I've always found the Riemann-Zeta function to be amusing. If you look it up, you'll often find it defined as:

Zeta(s) = Sum as n goes from 1 to infinity of 1/n^s.

Now think of this at s=-1 (as above):

Zeta(-1) = Sum as n goes from 1 to infinity of n = 1 + 2 + 3 + ...

which, of course, is infinity, and not -1/12!

( Of course, I realize that the RZ function is not defined like above except for real s > 0. For other regions in the complex plane, they define it via a completely valid mathematical procedure known as 'analytical continuation'. However, often people just define RZ as above, and then casually refer to quantities like Zeta(-1), which I find hilarious... )

 

[LucyR]

Zeta(s) = Sum as n goes from 1 to infinity of 1/n^s.

( Of course, I realize that the RZ function is not defined like above except for real s > 0.)

Doesn't s also have to be an integer for the function to reduce to this simple form?